Open Project Descriptions

What is NeuroDiffHub

Neurodiffhub is a platform that uses neural networks to store and disseminate solutions to differential equations. It includes a web application that allows users to search for specific differential equation, and an API that can be used to load and save solutions. The platform aims to provide a central repository for solutions to differential equations and make it easier for researchers and practitioners to access and use these solutions in their work.

Solving Differential Equations Using Neural Networks

Differential equations occur in various scientific and engineering domains. Most differential equations of practical interest are analytically intractable. Traditionally, differential equations are solved by numerical methods. Neural networks have been proven to be universal function approximators, suggesting the possibility of using ANNs to solve differential equations. These approaches are knows as Physics Informed Neural Networks (PINNs) have been one of the focus of our work. Those include NN solutions that preserve physical symmetries or symmetries in general, specialize networks for Hamiltonian systems, using GANs architectures to enhance the performance, a library that allows researchers to deploy these solutions. In this page you will find a summary of all current and future work.

Astromer

ASTROMER is a transformer-based model to create representations of astronomical light curves. ASTROMER is pre-trained self-supervised using hundreds of millions of unlabeled light curves. The learned weights can be easily adapted to other data by re-training ASTROMER on the new sources. The power of ASTROMER consists in using the representation to extract light curve embeddings that can enhance the training of other models, such as classifiers or regressors. Using ASTROMER embeddings decreases the computational resources needed while achieving state-of-the-art results. A python library includes all the functionalities employed in this work.

Computer Vision methods for the Event Horizon Telescope

In 2019, the Event Horizon Telescope Collaboration released the first-ever image of the M87* supermassive black hole. Accurate parameterization of images like this can provide new information regarding the dynamics of matter close to a black hole. Moreover, it can enable us to test theories of gravity and deepen our understanding of the magnetized relativistic jets created by the blackhole. In these projects, we deploy deep learning, to parameterize and estimate the physical parameters of M87*.

Reservoid Computing

Reservoir computers (RCs) are among the fastest to train of all neural networks, especially when compared to other recurrent neural networks. RC has this advantage while still handling sequential data exceptionally well. However, RC adoption has lagged other neural network models because of the model's sensitivity to its hyper-parameters (HPs). We developed \rctorch, a \pytorch based RC neural network package with automated HP tuning. In addition, we introduce an unsupervised reservoir computing (RC), capable of discovering approximate solutions that satisfy ordinary differential equations (ODEs).

Cosmologically Informed NNs

The field of machine learning has drawn increasing interest from various fields due to its methods' success in solving many different problems. An application of these has been to train artificial neural networks to solve differential equations without needing a numerical solver. In these works, we use artificial neural networks to represent solutions of the differential equations that govern the background dynamics of the Universe for four different models. We have applied these methods to various models such as the ΛCDM, a quintessence model with exponential potential, and the Hu-Sawicki f(R) model. We used the networks' solutions to perform statistical analyses to estimate the values of each model's parameters with observational data. Additionally, we use similar methods for holographic calculation of the bubble wall velocity in a cosmological phase transition, which is crucial to determine the resulting spectrum of GWs.

ADSML

he SAO/NASA Astrophysics Data System (ADS) is a digital library portal for researchers in astronomy and physics, operated by the Smithsonian Astrophysical Observatory (SAO) under a NASA grant. ADS maintains three bibliographic collections containing more than 15 million records covering publications in astronomy and astrophysics, physics, and general science, including all arXiv e-prints. The abstracts and full text of major astronomy and physics publications are indexed and searchable. At ADS ML, we are applying modern machine learning and natural language processing techniques to the ADS dataset to train astroBERT, a deeply contextual language model based on research at Google. Using astroBERT, we aim to enrich the ADS dataset and improve its discoverability; in particular, we are developing our own named entity recognition and concept discovery tools.

Other projects

Besides the projects described above, we have engaged in various other projects in particularly in astronomy and physics. Work on StellarNet , eigenvalue problems, embedding on galaxy images using auto-encoders and other topics are described in the page link provided.